Synthetic mega gyroscope

ABSTRACT

Systems and methods are disclosed herein for blind frequency synchronization. In one embodiment, a synthetic inertial measurement unit (IMU) is disclosed, comprising: a plurality of nodes wirelessly coupled to each other, each The method may further comprise: a wireless transceiver at a particular node for providing wireless communications with at least one other node of the plurality of nodes, configured to receive I and Q radio samples from the other node, and to determine a frequency offset of the other node based on the received I and Q radio samples, and to synchronize a clock at the particular node, a frequency offset synchronization module at the particular node coupled to the wireless transceiver, at the particular node, and an IMU sensor for determining rotation, acceleration, and speed of the particular node; and an IMU location estimation module for using time of arrival information assuming that the clock may be synchronized at the node, the determined distance, and the rotation, acceleration, and speed of the particular node received from the IMU sensor to determine the location of the nodes, thereby providing enhanced determination of location of the plurality of nodes.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of priority under 35 U.S.C. § 119(e)of U.S. Provisional Patent Application No. 62/825,402, filed Mar. 28,2019, and entitled “Synthetic Mega Gyroscope,” which is herebyincorporated by reference in its entirety for all purposes.Additionally, U.S. Pat. Nos. 9,048,979 and 9,048,980 are each herebyincorporated by reference in their entirety for all purposes.

BACKGROUND

As competitive consumer markets drive the price of mobile navigationdevices lower, an increasingly common choice for IMUs (inertialmeasurement units) is micro electro-mechanical systems (MEMS). Theirsmall size, low cost, light weight and low power consumption make theman attractive grade of IMU.

The single raw IMU measurements are normally mapped onto a common frame(i.e., a virtual frame) and typically processed using a filter such asthe extended Kalman filter (EKF). However, a single IMU's in-run biases,scale factors and high noise require an effective integration scheme tomitigate these errors [1].

The technologies that combine the multiple IMUs together to improve theestimation accuracy of body rotation and location have been receivingmore attention [2]. For example, a large stacked Kalman filter isconstructed of several IMUs. This filter construction allows forrelative information between the IMUs to be used as updates. The virtualIMU (VIMU) architecture is the most commonly used architecture in theliterature.

In the latest state-of-art multiple IMU technology, a federated filteris used to process each IMU as a local filter. The output of each localfilter is shared with a master filter, which in turn, shares informationback with the local filters.

SUMMARY

A synthetic inertial measurement unit (IMU) is disclosed, comprising: aplurality of nodes wirelessly coupled to each other, each The method mayfurther comprise: a wireless transceiver at a particular node forproviding wireless communications with at least one other node of theplurality of nodes, configured to receive I and Q radio samples from theother node, and to determine a frequency offset of the other node basedon the received I and Q radio samples, and to synchronize a clock at theparticular node, a frequency offset synchronization module at theparticular node coupled to the wireless transceiver, at the particularnode, and an IMU sensor for determining rotation, acceleration, andspeed of the particular node; and an IMU location estimation module forusing time of arrival information assuming that the clock may besynchronized at the node, the determined distance, and the rotation,acceleration, and speed of the particular node received from the IMUsensor to determine the location of the nodes, thereby providingenhanced determination of location of the plurality of nodes.

The IMU location estimation module may be for receiving IMU sensor datafrom the other node and using the received IMU sensor data, thedetermined distance to the other node, and the location of theparticular node to determine an inertial measurement of the other node.The synthetic IMU may be configured to determine an inertial measurementof each of the plurality of nodes and determine a synthetic inertialmeasurement for a single rigid body coupled to the plurality of theplurality of nodes. Each of the plurality of nodes may be located on oneof a plurality of aerial vehicles, and The method may further comprisetracking a location of each of the plurality of aerial vehicles usingthe determined location of the particular node and a determined locationof each of the plurality of nodes. The frequency offset synchronizationmodule may be configured to determine the frequency offset based on oneor more of: an angle of arrival of the received I and Q radio samples;and a cross-correlation between the received I and Q radio samples. Theplurality of nodes may be physically coupled to a plurality of:autonomous vehicles; drones; mobile vehicles; space vehicles, includingsatellites and landers; aircraft, including airborne drones and unmannedaerial vehicles (UAVs); mobile drone, including consumer robots andappliances; or autonomous balancing vehicles.

The IMU sensor may be configured to provide six-axis, nine-axis,acceleration, roll, yaw, pitch, or other orientation information. TheIMU sensor uses at least one of a gyroscope, an accelerometer, and amagnetometer. The synthetic IMU may be coupled to a Global PositioningSystem (GPS) positioning system for providing enhanced positioningaccuracy. The synthetic IMU may be configured to provide enhanced indoorpositioning accuracy for one or more of the plurality of nodes. The IMUlocation estimation module uses a stacked filter to combine IMUinformation from the particular node and from the other node. The IMUlocation estimation module may be located at a gateway. The plurality ofnodes uses properties of orthogonal frequency division multiplexing(OFDM) signaling to synchronize the nodes. The plurality of nodes usescross-correlation of orthogonal frequency division multiplexing (OFDM)signaling to synchronize the nodes.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of a general OFDM-based system.

FIG. 2 is a bit error rate (BER) performance of IEEE 802.11g in thepresence of carrier frequency offset (CFO), in accordance with someembodiments.

FIG. 3 illustrates a signal processing flow in some embodiments of animproved OFDM system.

FIG. 4 is a schematic illustration of the operations of equation (20),in accordance with some embodiments.

FIG. 5 is a flow chart of a frequency and phase synchronizationprocedure, in accordance with some embodiments.

FIG. 6 is a simulated performance plot of frequency synchronization ofan OFDM system with QPSK, in accordance with some embodiments.

FIG. 7 is a simulated performance plot of frequency synchronization ofan OFDM system with 64-QAM, in accordance with some embodiments.

FIG. 8 is a schematic system diagram showing a first scenario for usinga proposed synthetic IMU, in accordance with some embodiments.

FIG. 9 is a schematic system diagram showing a second scenario for usinga proposed synthetic IMU, in accordance with some embodiments.

FIG. 10A is a schematic diagram showing a wireless IMU network, inaccordance with some embodiments.

FIG. 10B is a schematic diagram showing a wireless IMU network with arigid body or with one gyroscope at center, in accordance with someembodiments.

DETAILED DESCRIPTION

A new multi-IMU (NMIMU) approach is described that allows for theinclusion of relative geometry constraints, such as relative position,velocity and attitude between IMUs. The use of these constraintsrepresents an advantage over the conventional technology called virtualIMU (VIMU) [3], since VIMU architectures fail to utilize this valuableinformation. The centralized filter consists of several individual localfilters, and are contained within one centralized filter, ultimatelyoperating as one. The significant improvement in location accuracy isachieved with the increase of number of IMUs with differentconfiguration of IMUs on rigid bodies.

The Challenges

The accuracy of each stacked filter architecture as a function of thenumber of IMUs is presented in [3]. Results indicate that the stackedfilter provides a linear increase in accuracy, while other architecturestypically have less improvement with the addition of more than threeIMUs. For any architectures of combining multiple IMUs, the gain oflocation estimation accuracy with multiple IMUs is quickly disappeareddue to the timing error as shown in [3].

Because of this issue, the incremental improvement for the NMIMU or VIMUfusion methods was modest. In this case the NMIMU with (Adaptive KalmanFilter) AKF provided the best solution, despite marginal timesynchronization issues.

Another shortcoming of existing technologies is the geometry of multipleIMUs which are limited to configurations called class I and II presentedin [4]. The commonly considered sensor geometries are based on regularpolyhedra. A polyhedron is regular if its faces are congruent regularpolygons and the polyhedral angles are all congruent. There are onlyfive regular polyhedra, as is well known.

IMU Sensor geometries where the sensor axes are placed along the normalsto the faces of these polyhedra are spherically symmetric. It ispossible to extend to other known configuration such as the satelliteand warship or another shape of rigid body with distributed IMUs. As itis shown that the current technology can only get benefit with a fewIMUs due to the time error among IMUs. In theory, the distributed IMUscan be combined to achieve better performance than single IMU. However,if the use of redundant IMUs proves to be of practical interest, astraightforward way to go is to use more independent, standard IMUs. Butthis is easier said than done. Time synchronization becomes critical,the relative orientation (position and attitude) of the IMUs must bemeasured and/or calibrated precisely, where the IMUs are positioned onthe object matters. And these geometric constraints have to betransferred to either the system dynamic observation model—the equationsof motion—or to the static observation model—the measurement equations[5].

The Possible Solutions

Our HSN network [6] provides the technologies which can accuratelysynchronize the distributed IMUs on wireless network as shown in FIG.10A. Since we can dynamically estimate the relative position among IMUs,this is equivalent to having the multiple IMUs attached to the rigidbody. The output of multiple IMUs equal to have one Gyroscope with highprecision, high cost and large size.

With our technology, the big challenge faced by existing SF or VIMUtechnologies due to the timing error among IMUs can be removed. Ourtechnology provides the unique solution of combining multiple IMUstogether to achieve high accuracy rotation and location estimationtechnology which is far beyond the current technologies. Anotheradvantage is that larger rigid bodies and many more IMUs can beincorporated in the wireless system, which is not feasible for existingtechnologies.

What we want to do are to extend the current multiple IMUs for variousrotation and location applications with the following features.

Based on the technique disclosed in U.S. Pat. No. 9,538,537, herebyincorporated by reference, the relative location of IMUs which areserved as each node in wireless mesh network, can be calculatedinstantaneously.

We provide a mathematical model for any arbitrary 3-D configuration ofIMUs, i.e., mathematical models for the accuracy and performance ofother shapes beyond the well-known shapes.

We provide wireless precise synchronization of all distributed IMUs.

With above feature, we enable a target object that could be any objectwith larger sizes, e.g., beyond meters.

In case that the distributed IMUs are attached to the rigid body withknown relative distance information, we can provide the synchronized IMUnetwork and combine the multiple IMUs measurement for betterperformance, as shown in FIG. 10 b;

In case that the multiple IMUs are attached to the multiple mobilenodes, we not only can provide the synchronization among the IMUs, butalso can calculate the relative positions among the IMUs for combining,as shown in FIG. 10 a . In this sense, we can dynamically process thedistributed IMUs even if they are not attached to a rigid body. Thisfeature opens a lot of applications beyond current technologies whichare mostly limited to the rigid body assumption.

Our system can be deployed in environments where the single highprecision gyroscope cannot be used due to its size and weight.

Our ultimate goal is to significantly improve navigation accuracy usingmultiple small, low cost IMU sensors (FIG. 10 a ) that can provideaccurate estimation of rotation and location that is equivalent to onehigh precision, high cost, heavy gyroscope (as shown in the middle ofFIG. 10 b ).

The stacked filter architecture in [3] is the way to combine themultiple IMUs. The sync among multiple IMUs is very important and has abig impact on the location performance as addressed in [3]. This is alsoa highlight spot from this application.

In this patent application, we intently to combine the mesh-networklocation algorithm with IMU to improve the location accuracy. Certainly,it will be beneficial to combine with more technologies such as GPS toenhance the performance in some applications when GPS is available.However, the study of the complexity and benefit will be taken intoaccount in details.

In some embodiments, the present disclosure could be equipped as partof: mobile vehicles; space vehicles, including satellites and landers;aircraft, including airborne drones and UAVs; any type of mobile drone,including consumer robots and appliances; measuring devices; cameras,including reconnaissance cameras, space cameras, aerial cameras; sportstraining technology; animation and motion capture; and/or autonomousbalancing devices.

In some embodiments, the present disclosure could be used in conjunctionwith GPS, GLONASS, any satellite- or non-satellite-based positiondetermination system, dead reckoning, inertial navigation systems,attitude and heading reference systems, etc. to provide a primary orredundant source of position information. In some embodiments, data frommultiple positioning systems as described in this paragraph andthroughout this disclosure could be combined using sensor fusion tosynthesize a more-accurate position as compared to a positiondetermination system without the use of the present disclosure. In someembodiments, the present disclosure could be used with a satellitepositioning system to provide location information when a clear line ofsight to satellites is not available, for example, when a vehicle isunderground or when a device is indoors.

As used herein, the word “synthetic” is used to mean a measurementdevice that incorporates measurements from a plurality of measuringdevices to produce a measurement that combines the plurality of inputs.

In operation, for example with a plurality of mobile users hostingsynced IMUs, they provide I/Q info and they can do sync, locally. Theyalso estimate time of arrival information and they will send thisinformation to a gateway. The gateway integrates the information usingthe more complicated algorithm.

Combining IMU data from multiple IMUs, e.g., at a location estimationmodule, is understood by the inventors to be well-known in the art andcan be accomplished at least using the algorithms detailed in, at least,Jared B. Bancroft and Gérard Lachapelle, “Data Fusion Algorithms forMultiple Inertial Measurement Units”, Sensors, MDPI, 2011; 11(7):6771-6798; Bancroft, J. B. Multiple Inertial Measurement UnitIntegration for Pedestrian Navigation. Ph.D. Thesis, Department ofGeomatics Engineering, The University of Calgary: Calgary, AB, Canada,2010; and “Redundant IMUs for Precise Trajectory Determination,”Colomina et al., Institute of Geomatics Generalitat de Catalunya &Universitat Politécnica de Catalunya Castelldefels, Spain, 2004, each ofwhich is hereby incorporated by reference in its entirety for allpurposes. Also hereby incorporated by reference in its entirety for allpurposes are the following: Manon Kok et al., “Using Inertial Sensorsfor Position and Orientation Estimation,” arXiv:1704.06053v2 10 Jun.2018; Sturza, Mark, “Skewed axis inertial sensor geometry for optimalperformance; geometry configuration,” American Institute of Aeronauticsand Astronautics, October 1988; and Jian Cui, Joshua Park, “Blindcarrier synchronization method for OFDM wireless communication systems”U.S. Pat. No. 9,538,537. In some embodiments the algorithm will takecare of this issue by detecting the failure of IMU, changing the combinealgorithm accordingly.

The inventors have also understood that the present technology can alsobe incorporated into a “mega gyro,” a single system that acts as asynthetic IMU for a large rigid body without the expense of one or morelarge gyroscopes. Having several small, inexpensive sensors that arehighly synchronized that can be used to provide a more-accurate IMU forany body of any size and any material is commercially valuable.

In some embodiments, a gateway can host a location estimation module. Inother embodiments the location estimation module can be at one or morenodes. In some embodiments time of arrival may be used without atimestamp or with a timestamp to estimate distance; to estimate distancewithout a timestamp, we use a previously-received wireless signal, suchas an OFDM signal, to synchronize the two nodes to enable precisedistance determination. In some embodiments an algorithm assumes thatprecise synchronization is achieved among the nodes. In someembodiments, the distance information among/between nodes is sent to thelocation estimation module.

The inventors have understood and appreciated that the prior art, namelyPark (U.S. Pat. No. 9,048,979), utilizes the orthogonality of I and Qwithin a received IQ signal in the time domain to characterize afrequency offset of the received IQ signal. However, the method of Parkis a single-carrier method and is not directly applicable to OFDMmodulated signals, which are multi-carrier, frequency modulated andmultiplexed. Orthogonality is present, but is not apparent from the Iand Q signals directly because the orthogonality is between I and Q ofeach subcarrier, not between the I and Q of the frequency-multiplexedsignal. The orthogonality of I and Q of the multiplexed signal is notindependent but is dependent on the underlying subcarriers. To solvethis problem, certain methods utilized herein separate out each of thepaired I and Q information signals that are present in thefrequency-multiplexed OFDM signal before computing cross-correlationaccording to the Park method. This results in a method that permitsblind frequency synchronization even for frequency-multiplexed signals.

In one embodiment, a system at a receive circuit is configured toperform synchronization based on a received signal as follows. Areceived signal is downconverted to baseband and broken up into a seriesof OFDM symbols, the number of symbols based on anarbitrarily-configured number sufficient to cause the synchronizationalgorithm to converge to within a certain error range, such as +/−5 ppb.The OFDM symbols are initially in the time domain. A fast Fouriertransform (FFT) is performed to turn these time domain symbols into OFDMsymbols in the frequency domain. As one OFDM symbol is made up of ablock of several frequency domain samples, a block of severaltime-domain samples is transformed via FFT into one OFDM symbol (basedon the preconfigured number of subcarriers in the OFDM signal).

Once a series of frequency domain OFDM symbols is created via FFT, eachof these symbols is fed into the method of Park and a cross-correlationis summed over each subcarrier over a number of the frequency domainOFDM symbols.

The cross-correlation is computed as the sum of the products of either asquare or absolute value of the in-phase and quadrature samples. Thissum may also be considered a cumulative phase measurement.

The cross-correlation is summed across the series of symbols and acrossall subcarriers to determine a frequency offset for the entire receivedsignal.

In some embodiments a subset of the received symbols may be discarded,for instance, repeated symbols that have been inserted for carriersynchronization, or symbols located by frequency in the middle of atransmission band. In some embodiments, the synchronization proceduremay be initiated at device power on, upon signal acquisition, atscheduled intervals, or upon detecting a loss of synchronization, insome embodiments with the same number of input samples being used eachtime the synchronization procedure is performed. The method is generallyapplicable to OFDM signals of different bandwidths, to QAM modulation orother types of modulation, and to other frequency domain multiplexingtechniques aside from OFDM.

The disclosed method is suitable for use with OFDM or other spreadspectrum multi-carrier transmission techniques. The disclosed method maybe applied across Wi-Fi, LTE, or other waveforms and radio transmissiontechniques. As described, the method may help to achieve superior timesynch, may help in implementation of a superior positioning methodthrough better time synchronization, and may permit better networksynchronization via more precise frequency offset correction.

As with Park, the disclosed method has the advantage that it is a purelyblind synchronization method that does not require a special beaconsignal or preamble, instead relying on a purely stochastic approach thatcan be adapted to virtually any signal. The disclosed method is alsosuperior to existing beacon-based methods in that it utilizes the entiresignal energy of the received signal.

The disclosed method works with any type of QAM modulation, e.g., QPSK,16 QAM, 64 QAM, 256 QAM, and other types of QAM modulation. Thedisclosed method also can use a subset of the available subcarriers toachieve synch, requiring only that a certain number of samples beavailable for processing. This permits the method to be used by anindividual user that may not have access to all available subcarriers,e.g., a user equipment (UE) on an LTE network, which typically only hasa small fraction of the available bandwidth at any time.

In this document, we consider the IEEE 802.11g WLAN OFDM system as anexample system which can be enhanced as follows. The methods andconclusions herein can be applied to any OFDM-based system. As usedherein, the term OFDM shall refer to any orthogonal frequency divisionmultiplexing scheme, including but not limited to commonly known OFDMschemes.

FIG. 1 shows a generic OFDM system block diagram. S/P stands for serialto parallel conversion, FFT stands for Fast Fourier Transform, P/Sstands for parallel to serial conversion, and IFFT stands for InverseFast Fourier Transform. Block 101 is a serial-to-parallel block whichreceives a series of digital bits from over a digital interface from acomputer or other digital device. S/P 101 takes the original bits, whicharrive already modulated (details not shown) in a single frequencydomain stream, splits them into several digital streams, and sends themto inverse FFT block 102.

IFFT 102 takes a set of digital bits (a “block”) in the time domain andapplies an IFFT function, turning them into symbols in the time domain.Parallel to serial block 103 takes the set of symbols from IFFT 102 andmultiplexes them into a single stream of symbols in the time domainusing an OFDM modulation. The multiplexed single stream is sent overchannel 104, which may be an air interface such as Wi-Fi or LTE, to areceiver. Details of the receive and transmit chains, such asupconversion and downconversion to/from carrier frequency,amplification, antennas, etc. are omitted in this diagram.

On the receive side, serial/parallel block 105 receives the output of anantenna and receive chain (not shown). The received signal is a seriesof symbols in the time domain. FFT 106 takes the received signal andtransforms it from the time domain to the frequency domain, then sendsit to parallel to serial block 107, which separates out the differentfrequency multiplexed symbol streams.

The sequence d=[d₀ d₁ d₂ . . . d_(N−1)] is a sequence of complex numbersthat represents the constellation points of data signals in thefrequency domain. The output of the IFFT block is the signal of Nsamples:s(k)=Σ_(i=0) ^(N−1) d _(k) e ^(j2πik/N) ;k=0,1, . . . ,N−1  (1)

Where d_(k) stands for OFDM symbol on the k'th subcarrier, N is thenumber of total sub-carriers. In case of AWGN channel and without CFOand SFO, the received signal can be expressed as:r(k)=s(k)+n(k),  (2)

for the OFDM demodulator, where n(k) is the complex Gaussian noise.

At the receiver side with ideal frame synchronization, the transmittedsignal can be recovered by FFT:R(i)=Σ_(k=0) ^(N−1) r(k)e ^(−j2πki/N) ;i=0,1, . . . ,N−1  (3)

Finally, we have:R(i)=d _(i) +n _(i) ,i=0,1, . . . ,N−1  (4)

where n_(i) is the complex Gaussian noise.

However, if the sampling frequencies at DAC and ADC are different due tothe transmitter and receiver using different local oscillators, CFO andSFO exist in the baseband signal at the output of the ADC. The impact ofthe sampling frequency difference on the baseband signal quality will beexplained next.

In the presence of a CFO of Δf_(s) and a SFO of ε_(s), the time domainsamples r(k) is given by:r(k)=Σ_(i=0) ^(N−1) d _(i) e ^(j2π(i+Δf) ^(s) ^()k(1+ε) ^(s) ^()/N);k=0,1, . . . ,N−1  (5)

Where Δf_(s) represents relative frequency offset normalized by fs/N,ε_(s) represents the relative sampling frequency error

${ɛ_{s} = \frac{\Delta f_{s}}{N}},$and fs is the sampling frequency. For simplicity, here it is assumedthat both CFO and SFO stem from the same frequency source error. Themethod presented in this document can be easily extended to the casethat both CFO and SFO are independent. Focusing the impact of SFO, atthe output of FFT, we have [2]:

$\begin{matrix}{{{R(m)} = {{e^{{- j}\;\pi\frac{N - 1}{N}mɛ_{s}}\frac{\sin\left( {\pi mɛ_{s}} \right)}{\sin\left( \frac{\pi mɛ_{s}}{N} \right)}d_{m}} + {W(m)} + {\sum\limits_{\underset{i \neq m}{i = 0}}^{N - 1}{d_{i}\frac{\sin\left( {\pi mɛ_{s}} \right)}{\sin\left( \frac{\pi\left\lbrack {{i\left( {1 + ɛ_{s}} \right)} - m} \right\rbrack}{N} \right)}e^{j\pi\frac{N - 1}{N}iɛ_{s}}e^{- \frac{j{\pi{({i - m})}}}{N}}}}}};} & (6) \\{\mspace{79mu}{{m = 0},1,\ldots\mspace{14mu},{N - 1}}} & \;\end{matrix}$

Three different effects can be observed from equation (6):

An amplitude attenuation by a factor of

$\frac{\sin\left( {\pi mɛ_{s}} \right)}{\sin\;\left( \frac{\pi mɛ_{s}}{N} \right)},$

A phase shift of symbol d_(m);

An inter-carrier interference (ICI) due to a loss of orthogonalitybetween the sub-carriers. (The third term in equation (6)).

The performance degradation in terms of SNR is shown in FIG. 2 , showinga BER of 256 QAM with a packet length of 1000 bytes. As an example,shown as plot 200, the IEEE 802.11g-based OFDM system is simulated withcoding rate of r=½. The standard requires that for frame length of 1000octets, the BER should be equal to or less than 10{circumflex over( )}(−5). Our system simulation results in FIG. 2 show that with carrierfrequency offset of 100 ppb, 4 dB SNR degradation is observed at BER of10{circumflex over ( )}(−5) versus a system without CFO. If thefrequency offset is larger than 150 ppb, the system can never reach aBER of 10{circumflex over ( )}(−5) requirement even with high SNR.

FIG. 3 illustrates a signal processing flow in some embodiments of animproved OFDM system. As shown in FIG. 3 , we use IEEE 802.11g as anexample to show signal processing flow in an exemplary OFDM system. Area310 represents a series of steps performed at a transmitting node andarea 320 represents a receiving node. Signal 301 is a digital basebandfrequency domain signal, numbered d_(l,k), where l is the symbol numberand k is a sample number. Signal 302 is also a digital basebandfrequency domain signal, where l is the symbol number and represents thelast in a series of symbols from 1 to l. The value of l can be variedbased on configuration of the system, with tradeoffs: without asufficient number of symbols, synchronization may not be achieved to adesired level of accuracy, but processing more symbols requires greatersampling time and processing time.

At the transmitter side, frequency modulated signals d_(l,k)=[d_(l,1)d_(l,2) . . . d_(l,64)] are transformed to a time domain signal s(l,k),k=1, . . . , 64, by IFFT, shown as samples 305. The last 16 samples ofs(l,k), 303 is inserted at the front of the 64-sample block signal toform one OFDM symbol in the time domain. This operation results insimple channel equalization in OFDM system. Samples 303, 305 are a firstsymbol in the frequency domain and the time domain, respectively, andsamples 304, 306 are an lth symbol in the frequency and the timedomains, respectively.

At the receiver side, data sequence r(l,k) is received in time domainafter ADC. R(l,i) is obtained after FFT based on frame synchronizationinformation. Symbol 307 in the time domain is 80 samples long due to aneed for frame synchronization; after FFT into the frequency domain,transformed symbol 309 is 64 samples long. Symbols 307 and 309 are afirst symbol, i.e., l=1; symbols 308 and 310 are an lth symbol for thehighest allowed value of l, in the time domain and the frequency domain,respectively. The coefficients of symbol 308 reflect the fact that thetotal number of samples collected for any one iteration of the presentoffset detection/synchronization algorithm is l*80.

Assuming the sampling frequency is Fs and the FFT size is N for the OFDMsystem, the received signal in the frequency domain with frequencyoffset error of ε can be expressed as in [4], as:

$\begin{matrix}{{{R\left( {l,i} \right)} = {{e^{{- j}v_{l}{ɛ{({1 + \frac{i}{N}})}}}H_{i}d_{l,i}} + {W\left( {l,i} \right)}}},} & (7) \\{{i = 0},1,\ldots\mspace{14mu},{63;{l = 1}},2,\ldots\mspace{14mu},N_{{of}\;{dm}}} & \;\end{matrix}$

Where,

${v_{l} = {\pi\frac{N - 1 + {2N_{l}}}{N}}};$N_(l)=lN_(s)+N_(g); l is number of OFDM symbols, i is the number ofsubcarrier indices within each OFDM symbol, N_(g) is the guard intervallength with N_(s)=N+N_(g), N_(ofdm) is the number of OFDM symbols in onedata frame, and H_(i) is the channel response in subcarrier of i. Forexample, in an IEEE 802.11g WLAN system, N=64; N_(g)=16. Again, here itassumed that both CFO and SFO are from the same local oscillator error.

Removing the constant phase rotation applied to every signal and thenoise term, the equation (7) can be simplified to:

$\begin{matrix}{{{R\left( {l,i} \right)} = {e^{{- j}\; 2\;\pi\;{lN}_{s}\;{ɛ{({1 + \frac{i}{N}})}}}H_{i}d_{l,i}}},{i = 0},1,\ldots\mspace{14mu},{63;{l = 1}},2,\ldots\mspace{14mu},N_{{of}\;{dm}}} & (8)\end{matrix}$

For a given i=m, we can define a new sequence in time index of l bytaking every 64th sample from R(l,i) as:R(l,m)=e ^(−j2πlε) ^(m) H _(m) d _(l,m) ,l=1,2, . . . ,N _(ofdm)  (9)

where

${ɛ_{m} = {ɛ{N_{s}\left( {1 + \frac{m}{N}} \right)}}}.$

Since ε_(m) is unknown, we can form a new sequence with potentialfrequency offset of ε′. Define Δε_(m)=ε_(m)−ε′_(m) and

$ɛ_{m}^{\prime} = {ɛ^{\prime}{{N_{s}\left( {1 + \frac{m}{N}} \right)}.}}$Multiplying Equation (9) by e^(j2πlε′), we have:U(l,m,ε′)=R(l,m)e ^(j2πlε′) ^(m) =e ^(−j2πlΔε) ^(m) H _(m) d _(l,m),l=1,2, . . . ,N _(ofdm)  (10)

We define the real and imaginary part of equation (9) as:I(l,m)=real(H _(m) d _(l,m))Q(l,m)=imag(H _(m) d _(l,m)),l=1,2, . . . ,N _(ofdm)  (11)

We rewrite the real and imaginary part of equation (10) asI _(R)(l,m,ε′)=real(U(l,m,ε′))=I(l,m)cos(2πlΔε _(m))−Q(l,m)sin(2πlΔε_(m))Q _(R)(l,m,ε′)=imag(U(l,m,ε′))=Q(l,m)cos(2πlΔε _(m))+I(l,m)sin(2πlΔε_(m))  (12)

We define the objective function as the following cross-covariancebetween I_(R)(l,m,ε′)² and Q_(R)(l,m,ε′)²:J(Δε_(m))=C(A,B)=Σ_(l){(A−μ _(A))(B−μ _(B))},  (13)

where:A={I _(R)(l,m,ε′)}² and B={Q _(R)(l,m,ε′)}²  (14)

We also define:Σ_(l) {A}=μ _(A) and Σ_(l) {B}=μ _(B)  (15)

with the assumption that μ=μ_(A)=μ_(B).

Following the same procedure in [1], we have:

$\begin{matrix}{{J\left( {\Delta ɛ_{m}} \right)} = {{\mu^{2}\Sigma_{l}\left\{ \frac{1 + {\cos 8\pi\Delta ɛ_{m}l}}{2} \right\}} - \mu^{2}}} & (16)\end{matrix}$

The cross-covariance of J(Δε_(m)) becomes zero when Δε_(m)=0, whichequals to ε′=ε in equation (10).

In the same way, we can define the objective function as:J(ε′)=Σ_(m) J(Δε_(m))  (17)

In equation (17), the summation is made for all possible non-empty binindex of m. For example, in an IEEE 802.11g system, only 52 out 64 binsare used. In this case, we can fully use all data from all availablebins in the frequency synchronization. It turns out that, as expected,higher accuracy synchronization is achieved by using more bins.

Mathematically, the equation (16) can also be rewritten to find ε_(m),as maximum:

$\begin{matrix}{{\max\limits_{ɛ_{m}}{J_{1}\left( {\Delta ɛ_{m}} \right)}} = {{\sum\limits_{l}\left\{ {AB} \right\}} = {\mu^{2}{\sum\limits_{l}\left\{ \frac{1 + {\cos 8\pi\Delta ɛ_{m}l}}{2} \right\}}}}} & (18)\end{matrix}$

The objective function will achieve its maximum value when ε′_(m)=ε_(m).In the same way, the equation (17) can be rewritten asJ(ε′)=Σ_(m)Σ_(l) {AB}  (19)

where l is the index for OFDM symbols, and m is the index for thesubcarrier index within each OFDM symbol.

Next, we will provide variations of equation (19). It is noted that theequation (19) can be written as:

$\begin{matrix}{{\max\limits_{ɛ^{\prime} \in {\lbrack{f_{1};f_{2}}\rbrack}}{J\left( ɛ^{\prime} \right)}} = {{\sum\limits_{m}{\sum\limits_{l}\left\{ {AB} \right\}}} = {\sum\limits_{m}{\sum\limits_{l}{\left\{ {I_{R}\left( {l,m,ɛ^{\prime}} \right)} \right\}^{2}\left\{ {Q_{R}\left( {l,m,ɛ^{\prime}} \right)} \right\}^{2}}}}}} & (20)\end{matrix}$

Where [f1, f2] is the frequency range of interest. Equation (20) can berewritten as:

$\begin{matrix}{{\max\limits_{ɛ^{\prime} \in {\lbrack{f_{1};f_{2}}\rbrack}}{J\left( ɛ^{\prime} \right)}} = {{\sum\limits_{m}{\sum\limits_{l}\left\{ {AB} \right\}}} = {\sum\limits_{m}{\sum\limits_{l}{{{I_{R}\left( {l,m,ɛ^{\prime}} \right)}{Q_{R}\left( {l,m,ɛ^{\prime}} \right)}}}^{2}}}}} & (21)\end{matrix}$

and mathematically equation (21) is equivalent to maximizing thefollowing objective function:

$\begin{matrix}{{\max\limits_{ɛ^{\prime} \in {\lbrack{f_{1};f_{2}}\rbrack}}{J\left( ɛ^{\prime} \right)}} = {\sum\limits_{m}{\sum\limits_{l}{{{I_{R}\left( {l,m,ɛ^{\prime}} \right)}{Q_{R}\left( {l,m,ɛ^{\prime}} \right)}}}}}} & (22)\end{matrix}$

It is also the same as maximizing this second objective function aswell:

$\begin{matrix}{{\max\limits_{ɛ^{\prime} \in {\lbrack{f_{1};f_{2}}\rbrack}}{J\left( ɛ^{\prime} \right)}} = {\sum\limits_{m}{\sum\limits_{l}{{{I_{R}\left( {l,m,ɛ^{\prime}} \right)} \parallel {Q_{R}\left( {l,m,ɛ^{\prime}} \right)}}}}}} & (23)\end{matrix}$

FIG. 4 is a schematic illustration of the operations of equation (20),in accordance with some embodiments. OFDM symbol #1 401 is made up ofmultiple frequency subcarriers 402, 404, 406, with subcarrier 402 havingsubcarrier number 1 and subcarrier 406 having subcarrier number 64, thehighest subcarrier number in this diagram. Similarly, OFDM symbol #2 403and all symbols up to and including OFDM symbol #1 405 are also made upof 64 subcarriers.

On the right of the diagram, equation 412 reflects the fact that thesquared absolute values (i.e., the cross-correlation according to Park)of every symbol having subcarrier number 1 are summed. Equations 414 and416 reflect the summation of cross-correlations of every subcarrieracross each OFDM symbol, with equation 420 reflecting the summation ofcross-correlations across both every subcarrier and every symbol. Insome embodiments, squared absolute values may be used; in otherembodiments, absolute values may be used without squaring, according toPark.

FIG. 5 is a flow chart of a frequency and phase synchronizationprocedure, in accordance with some embodiments. The detailed frequencysynchronization procedure is as follows.

At step 501, the algorithm initialization function 501 defines thealgorithm parameters used in synchronization process.

Nsamp is the total number of samples used in the synchronizationprocess.

[f1 f2] is the target frequency range of frequency offset. For example,the IEEE 802.11g standard defines the maximum frequency offset in termof ppm to be −/+20 ppm. In this case, f1=−48 kHz, f2=48 kHz.

Δf is the step size for searching the frequency range of interest. Thesethree numbers are adaptively reduced to minimize complexity ofcomputation and meet accuracy requirements for specific communicationsystems.

Initial phase value. This is set to zero. In application, there alwaysexists a constant phase difference between the transmitter and receiverin addition to the CFO and SFO. The phase difference is caused by thedifferent sampling time at the transmitter and receiver, and airpropagation. The phase difference sometimes also refers to the symboltiming and needs to be aligned at the receiver.

ΔØ is the step size for phase alignment. This number, like Δf, isadaptively adjusted. A larger value means fast alignment but with lessresolution. A small value means high resolution and more computationalcomplexity. It is normally selected to be a larger ΔØ at the initialphase alignment stage and a smaller ΔØ for higher accuracy of phasealignment.

At step 511, a signal of r(k) in equation (2) is acquired, which can besampled at 1×, 2× or 4× of the basic sample rate at the ADC output inthe receiver.

At step 512, the time domain signal r(k) is converted into a frequencydomain signal of R(l,i) by FFT operation based on frame synchronizationinformation. l is the number of OFDM symbols within one data frame and iis the subcarrier index within each OFDM symbol.

At step 521, firstly, the operation defined in equation (20) to crossover the number of OFDM symbols l and the subcarrier index i for thepossible frequency range and defined step size is performed. The outputsof step 521 are the maximum value of equation (20) and its associatedfrequency. Secondly, the phase alignment is rotated with equation (20)until a new max value occurs. Details regarding this phase alignmentstep are addressed in U.S. Pat. No. 9,048,979, Park. This summationacross both all samples and all symbols expresses the use ofcross-correlation or orthogonality to determine phase offset.

At step 532, the direction of phase change and its resolution are tuned.The increase or decrease of phase value will be determined by thecomparison between the max values of equation (20) with the differingphase value. For example, at the kth value of phase, if the max value ofJ1 is less than the max value of J1 at the (k−1)th phase value, thephase value will be decreased at the next round of search. ΔØ is thestep size for the phase alignment process.

At step 551, it is determined whether the synchronization process iscomplete. If the differences of (M) consecutive maximum values ofequation (20) are less than a predefined threshold value, thesynchronization process finishes. Otherwise, processing goes to circuit142 by reducing the frequency search resolution and performing thesynchronization process using circuit 121 again. A control operation isalso performed to determine if an update is needed, or if a newsynchronization process should be started. A new update orsynchronization process may be performed, for example, upon power on ofan antenna, upon connection to a new radio source, after a certainconfigurable time interval, or after other events that would be expectedto produce de-synchronization.

The systems and methods presented here can be applied to any singlecarrier system with complex signals at the receiver, and specifically toa multi-carrier based OFDM communication system. This method can bedescribed as a blind synchronization method for a single carrier OFDMbased system. For a given OFDM based system, only frame synchronizationinformation is needed. After frame synchronization is done, eachtime-domain OFDM symbol can be detected and FFT operation can be appliedwithout decoding the symbols. The raw samples after FFT can be used forfrequency synchronization directly without any additional information.

For most OFDM systems, some form of channel equalization is alsopossible using known preambles/pilots before high-precision CFO and SFOcorrection is done. In such cases, the channel components in equation(10) R(l,i) can be removed. Simulations show that the performance of ourmethod can be improved in conjunction with channel equalizationtechniques.

System Simulation Results

To demonstrate the performance of the proposed method for the frequencysynchronization, simulation is conducted using an IEEE 802.11g system asan example. QPSK and 64-QAM signals are used in the simulation to showthat the method can work for any type of modulation signal in the OFDMsystem. Only frame synchronization information is used in the simulationfor the random chosen frequency offset. It is apparent from FIGS. 6 and7 that for both 4-QAM and 64-QAM OFDM signals, the accuracy of frequencyestimation can be achieved within single digit of ppb levels with a SNRof only 5 dB.

FIG. 6 is a simulated performance plot of frequency synchronization ofan OFDM system with QPSK, in accordance with some embodiments. Thedepicted system is an OFDM system with a 4-QAM signal, with a SNR of 5dB. After roughly 12 simulation runs, it appears that the simulation hassettled down to an estimation error of roughly 3 to 5 parts per billion.

FIG. 7 is a simulated performance plot of frequency synchronization ofan OFDM system with 64-QAM, in accordance with some embodiments. Withthe same resolution and SNR, the figure shows an OFDM system with a64-QAM signal. After the same number of simulation runs as in FIG. 6 ,there does not appear to be a convergence of estimation error. This isat least partially because at higher QAM levels, the deviation ofcross-correlation/orthogonality of I and Q from zero is much smaller,resulting in a need to collect more data to reach the same level ofestimation error.

Applications

The proposed frequency synchronization method can be applied to anysingle carrier or multicarrier communication system where the receiversignal is complex, such as, widely used wireline and wireless systemslike ADSL, WLAN, WiMax, LTE, DVB-T, etc.

The disclosed method can be used in OFDM based backhaul systems, wherethe base station and user equipment can both use this technology tosynchronize both frequency and timing first, prior to starting highspeed data transmission. This will reduce interference among users andincrease spectrum reuse efficiency.

The disclosed method can be applied to LTE systems. Even whensynchronized both in frequency and timing between a user and a basestation, all users transmit at different timing based on their distancefrom the base station, to ensure that all signals arrive at the basestation at the same time. The disclosed method makes multi-userdetection at base station (up-link) more feasible with less complexityof receiver design. It not only reduces the interference among users,but also keeps the orthogonality between subcarrier signals for eachuser.

The disclosed method can be applied to any communication system wherefrequency synchronization is needed to boost the data throughput,increase spectrum efficiency and reduce the complexity of receivers forCFO and CFO estimation and correction, such as IEEE 802.11g, 802.11n,and 802.11ac systems.

The disclosed two stage method can be applied to frequencysynchronization using the methods proposed here for initial frequencysynchronization and timing acquisition, and fine-tuning frequency andtiming information during connection establishment and continuedcommunication.

The disclosed two stage method can be applied to frequencysynchronization using other methods for coarse frequency and timingacquisition, and using the disclosed methods for fine-tuning frequencyand timing information during connection establishment and continuedcommunication.

The disclosed frequency and phase synchronization process can use asingle bin, a subset of bins, or all available bins in a OFDM system.

In the frequency synchronization update stage, a prior signal can beused in conjunction with a current available signal based on either asliding window or weighted average method.

FIG. 8 is a schematic system diagram showing a first scenario for usinga proposed synthetic IMU, in accordance with some embodiments. OFDMtransmitter 801 is connected to transmit antenna 802, and sendsOFDM-multiplexed signals to receive antenna 803. Receive antenna 803 isconnected to low noise amplifier (LNA) 804, which amplifies the lowpower signal received from antenna 803, and sends it to mixer 805. Mixer805 performs downconversion from the carrier frequency to baseband. Indoing so, mixer 805 utilizes the frequency generated by oscillator 809,which has frequency offset that is desired to be compensated. Mixer 805outputs an analog baseband signal to analog to digital converter (ADC)806; stages 803, 804, and 805 constitute the analog baseband, labeledhere as section 12.

Continuing on in digital baseband section 813, ADC 806 receives its ownclock signal from fractional n frequency synthesizer 810. Synthesizer810 accepts a clock input from oscillator 809 (which is subject tofrequency offset) and converts that clock input to a sample rateappropriate for the ADC, which then uses the sample rate to sample theanalog input signal and transform it into a digital signal, i.e., a setof samples. ADC 806 then passes the digital signal to frame sync module807. Frame sync module 807 determines the boundaries of each frame, asdescribed elsewhere herein, by comparing symbols and identifying frameedges based on repeated symbols. The number of symbols to be bufferedfor frame synchronization is often described by the relevant OFDMstandard. Once frame alignment is achieved, complete frames are sent toa OFDM demodulator to be turned from symbols into digital data. Clocksync 808 is shown as performing clock sync at the particular node.

Frequency synchronization module 811 is a module performing steps asdescribed herein for creating synchronization. It accepts digitalsamples from frame sync module 807 and determines, based oncross-correlating I and Q across samples and subcarriers as describedherein, whether any phase offset or frequency offset is present, andthis offset signal can be fed back to oscillator 809, in someembodiments, to correct for offset.

In operation, at the initial communication stage, such as a scan,association or handshaking process, all users are synchronized with theAP/Base-station by tuning their local oscillators to match frequency andtiming from the AP or base station, as shown by the dashed line betweensynchronization module 811 and oscillator 809 in FIG. 8 . The systemwill maintain synchronization status by continuing to update frequencyand time whenever it is needed. In this case, our CFO and SFO estimationand correction method can be used to fine-tune the oscillatorcontinuously at the receiver.

FIG. 9 is a schematic system diagram showing a second scenario for usinga proposed synthetic IMU, in accordance with some embodiments. In thissecond scenario, it is assumed that adjusting the local oscillator isnot feasible, and that the CFO and SFO correction should be done in thedigital domain. Fine frequency offset tuning could instead be appliedduring a data communication period as part of a frame synchronizationand channel equalization procedure. Analog baseband receive chain 912consists of antenna 901, low noise amplifier 902, and mixer 903, whichoperate as described in relation to FIG. 8 . Mixer 903 receives acarrier frequency from oscillator 909 and subtracts it from the receivedsignal to downconvert the signal to baseband. Oscillator 909 has afrequency offset, but is not able to receive a compensation signal. Inthis case, coarse synchronization can be performed between thetransmitter and receiver in the initial communication stage using themethod proposed herein or using a conventional method. An analogbaseband signal is sent to ADC 904.

Digital baseband 913 consists of ADC 904, which receives the analogsignal and converts it to a digital signal; fractional N frequencysynthesizer 910, which converts oscillator 909's signal to a samplingrate for ADC 904; frame synchronization module 905, for identifying OFDMframe edges; CFO/SFO correction module 906, to be described below; andOFDM demodulator 908, which outputs bits to the main processor of thedigital device (not shown).

Frequency synchronization module 911 receives digital symbols from framesync module 905 and identifies frequency offset through thecross-correlation method described herein. However, since the oscillatordoes not receive the offset correction signal, it is sent to a newmodule, CFO/SFO correction module 906, which applies correction to thesignal in the digital domain before it is sent to the OFDM demodulator908.

A separate IMU 912 is present on the node. IMU location combiner assumesa synced clock 906 and receives IMU data from IMU 912 to estimatelocation. This may be done on the node or at a separatelocation/node/gateway.

FIG. 10A is a schematic diagram showing a wireless IMU network, inaccordance with some embodiments. Multiple nodes 1011-1019 are shown inwireless communication and in full sync, acting as a synthetic IMU.

FIG. 10B is a schematic diagram showing a wireless IMU network with arigid body or with one gyroscope at center, in accordance with someembodiments. 1029 is a large gyro that is integrated into the syntheticIMU.

From the foregoing, it will be clear that the present invention has beenshown and described with reference to certain embodiments that merelyexemplify the broader invention revealed herein. Certainly, thoseskilled in the art can conceive of alternative embodiments. Forinstance, those with the major features of the invention in mind couldcraft embodiments that incorporate one or major features while notincorporating all aspects of the foregoing exemplary embodiments.

In the foregoing specification, specific embodiments have beendescribed. However, one of ordinary skill in the art appreciates thatvarious modifications and changes can be made without departing from thescope of the invention as set forth in the claims below. Accordingly,the specification and figures are to be regarded in an illustrativerather than a restrictive sense, and all such modifications are intendedto be included within the scope of present teachings.

The benefits, advantages, solutions to problems, and any element(s) thatmay cause any benefit, advantage, or solution to occur or become morepronounced are not to be construed as a critical, required, or essentialfeatures or elements of any or all the claims. The invention is definedsolely by the appended claims including any amendments made during thependency of this application and all equivalents of those claims asissued.

Moreover, in this document, relational terms such as first and second,top and bottom, and the like may be used solely to distinguish oneentity or action from another entity or action without necessarilyrequiring or implying any actual such relationship or order between suchentities or actions. The terms “comprises,” “comprising,” “has”,“having,” “includes”, “including,” “contains”, “containing” or any othervariation thereof, are intended to cover a non-exclusive inclusion, suchthat a process, method, article, or apparatus that comprises, has,includes, contains a list of elements does not include only thoseelements but may include other elements not expressly listed or inherentto such process, method, article, or apparatus. An element proceeded by“comprises . . . a”, “has . . . a”, “includes . . . a”, “contains . . .a” does not, without more constraints, preclude the existence ofadditional identical elements in the process, method, article, orapparatus that comprises, has, includes, contains the element. The terms“a” and “an” are defined as one or more unless explicitly statedotherwise herein. The terms “substantially”, “essentially”,“approximately”, “about” or any other version thereof, are defined asbeing close to as understood by one of ordinary skill in the art, and inone non-limiting embodiment the term is defined to be within 10%, inanother embodiment within 5%, in another embodiment within 1% and inanother embodiment within 0.5%. The term “coupled” as used herein isdefined as connected, although not necessarily directly and notnecessarily mechanically. A device or structure that is “configured” ina certain way is configured in at least that way, but may also beconfigured in ways that are not listed.

It will be appreciated that some embodiments may be comprised of one ormore generic or specialized processors (or “processing devices”) such asmicroprocessors, digital signal processors, customized processors andfield programmable gate arrays (FPGAs) and unique stored programinstructions (including both software and firmware) that control the oneor more processors to implement, in conjunction with certainnon-processor circuits, some, most, or all of the functions of themethod and/or apparatus described herein. Alternatively, some or allfunctions could be implemented by a state machine that has no storedprogram instructions, or in one or more application specific integratedcircuits (ASICs), in which each function or some combinations of certainof the functions are implemented as custom logic. Of course, acombination of the two approaches could be used.

Moreover, an embodiment can be implemented as a computer-readablestorage medium having computer readable code stored thereon forprogramming a computer (e.g., comprising a processor) to perform amethod as described and claimed herein. Examples of suchcomputer-readable storage mediums include, but are not limited to, ahard disk, a CD-ROM, an optical storage device, a magnetic storagedevice, a ROM (Read Only Memory), a PROM (Programmable Read OnlyMemory), an EPROM (Erasable Programmable Read Only Memory), an EEPROM(Electrically Erasable Programmable Read Only Memory) and a Flashmemory. Further, it is expected that one of ordinary skill,notwithstanding possibly significant effort and many design choicesmotivated by, for example, available time, current technology, andeconomic considerations, when guided by the concepts and principlesdisclosed herein will be readily capable of generating such softwareinstructions and programs and ICs with minimal experimentation.

The Abstract of the Disclosure is provided to allow the reader toquickly ascertain the nature of the technical disclosure. It issubmitted with the understanding that it will not be used to interpretor limit the scope or meaning of the claims. In addition, in theforegoing Detailed Description, it can be seen that various features aregrouped together in various embodiments for the purpose of streamliningthe disclosure. This method of disclosure is not to be interpreted asreflecting an intention that the claimed embodiments require morefeatures than are expressly recited in each claim. Rather, as thefollowing claims reflect, inventive subject matter lies in less than allfeatures of a single disclosed embodiment. Thus the following claims arehereby incorporated into the Detailed Description, with each claimstanding on its own as a separately claimed subject matter.

The invention claimed is:
 1. A synthetic inertial measurement unit(IMU), comprising: a plurality of nodes wirelessly coupled to eachother, each further comprising: a wireless transceiver at a particularnode for providing wireless communications with at least one other nodeof the plurality of nodes, configured to receive I and Q radio samplesfrom the other node, and to determine a frequency offset of the othernode based on the received I and Q radio samples, and to synchronize aclock at the particular node, a frequency offset synchronization moduleat the particular node coupled to the wireless transceiver, at theparticular node, and an IMU sensor for determining rotation,acceleration, and speed of the particular node; and an IMU locationestimation module for using time of arrival information assuming thatthe clock is synchronized at the node, the determined distance, and therotation, acceleration, and speed of the particular node received fromthe IMU sensor to determine the location of the nodes, thereby providingenhanced determination of location of the plurality of nodes.
 2. Thesynthetic IMU of claim 1, wherein the IMU location estimation module isfor receiving IMU sensor data from the other node and using the receivedIMU sensor data, the determined distance to the other node, and thelocation of the particular node to determine an inertial measurement ofthe other node.
 3. The synthetic IMU of claim 1, wherein the syntheticIMU is configured to determine an inertial measurement of each of theplurality of nodes and determine a synthetic inertial measurement for asingle rigid body coupled to the plurality of the plurality of nodes. 4.The synthetic IMU of claim 1, wherein each of the plurality of nodes islocated on one of a plurality of aerial vehicles, and further comprisingtracking a location of each of the plurality of aerial vehicles usingthe determined location of the particular node and a determined locationof each of the plurality of nodes.
 5. The synthetic IMU of claim 1,wherein the frequency offset synchronization module is configured todetermine the frequency offset based on one or more of: an angle ofarrival of the received I and Q radio samples; and a cross-correlationbetween the received I and Q radio samples.
 6. The synthetic IMU ofclaim 1, wherein the plurality of nodes are physically coupled to aplurality of: autonomous vehicles; drones; mobile vehicles; spacevehicles, including satellites and landers; aircraft, including airbornedrones and unmanned aerial vehicles (UAVs); mobile drone, includingconsumer robots and appliances; or autonomous balancing vehicles.
 7. Thesynthetic IMU of claim 1, wherein the IMU sensor is configured toprovide six-axis, nine-axis, acceleration, roll, yaw, pitch, or otherorientation information.
 8. The synthetic IMU of claim 1, wherein theIMU sensor uses at least one of a gyroscope, an accelerometer, and amagnetometer.
 9. The synthetic IMU of claim 1, wherein the synthetic IMUis coupled to a Global Positioning System (GPS) positioning system forproviding enhanced positioning accuracy.
 10. The synthetic IMU of claim1, wherein the synthetic IMU is configured to provide enhanced indoorpositioning accuracy for one or more of the plurality of nodes.
 11. Thesynthetic IMU of claim 1, wherein the IMU location estimation moduleuses a stacked filter to combine IMU information from the particularnode and from the other node.
 12. The synthetic IMU of claim 1, whereinthe IMU location estimation module is located at a gateway.
 13. Thesynthetic IMU of claim 1, wherein the plurality of nodes uses propertiesof orthogonal frequency division multiplexing (OFDM) signaling tosynchronize the nodes.
 14. The synthetic IMU of claim 1, wherein theplurality of nodes uses cross-correlation of orthogonal frequencydivision multiplexing (OFDM) signaling to synchronize the nodes.